Linear optics ID compensation on the 3 GeV storage ring at MAX IV Laboratory

Abstract

MAX IV Laboratory is a modern synchrotron light source, providing synchrotron radiation used in a wide range of experiments. The production of synchrotron radiation used in experiments typically takes place in insertion devices (IDs), in which an oscillatory motion is induced in traversing electrons, stimulating the emission of synchrotron radiation. IDs consist of a periodic arrangement of magnets, and inevitably have an undesired impact on the electron beam. This report is an account of an attempt to implement and evaluate a first proof-of-concept compensation scheme on the 3 GeV ring for one of the lowest-order perturbations caused by the effects of IDs, namely the transverse beam size, largely governed by the betatron (or beta, β) functions.

The approach to eliminate perturbations in β functions relies on adjusting strengths of beam-focusing quadrupole magnets adjacent to the ID. In this way, the β functions in most of the storage ring can be restored to nominal values. Two different approaches were used to determine the quadrupole strength adjustments required for eliminating β function deviations. The first employs the use of so-called kickmaps to model the effects of IDs. It is an entirely theoretical approach, in which quadrupole adjustments are determined through numerical optimization on a model of the magnetic lattice comprising the storage ring. ID compensation using this approach has been studied at MAX IV Laboratory in the past, and has been used to develop and implement the ID compensation scheme on the 1.5 GeV ring.

The second approach to determining quadrupole adjustments was developed as part of this project, and consists of an optimization scheme on the online accelerator that iteratively measures β functions and calculates adjustments, eventually converging to the noise floor of the perturbation measurement. This approach is unconventional, and should be viewed as a proof of concept.

Evaluations of β function compensation were performed on quadrupole adjustments obtained from both methods. In this study, the kickmap-based compensation proved largely unsuccessful in eliminating perturbations in β functions, achieving reduction in root mean square RMS(∆β/β) of no more than 47% for any one ID. In one of the initial tests, the online algorithm was used to reduce RMS(∆β/β) by 90% in optimal conditions. The current implementation of the online compensation is known to be limited by BPM timing configuration and noise.

Popular Abstract

Modern synchrotron light sources provide a vast array of experiments with light to probe material structures at very small scales. To produce synchrotron light for experiments, the beam of electrons is sent through a magnetic device which causes electrons to violently wiggle back back-and-forth. Unfortunately, due to imperfections in the magnetic fields of these devices, some properties of the electron beam passing through them will undergo undesired change. One negatively affected property is the beam size. Errors in the beam size can be a severe detriment to the facility as a whole, leading to beam instabilities and losses. For this and more reasons, the beam size needs to be corrected. This short essay is a description of an approach that was taken at MAX IV Laboratory to restore the electron beam size.

Synchrotron light sources consist of a ring-like structure, around which a beam of electrons travels at nearly the speed of light. As the purpose of the ring-like structure in a synchrotron light source is to store electrons in a beam, it has been coined (admittedly uncreatively) electron storage ring, or simply storage ring. In storage rings, powerful magnets are used to control the properties of the electron beam. In this project, the main property of interest is the (transverse) beam size, which describes the amount of space taken up by electrons in the beam in the horizontal and vertical directions. An interesting property of the beam size is that it varies from point to point in the storage ring. It can be thought of in analogy to rays of light traveling through a series of lenses, undergoing repeated focusing and defocusing. Much like lenses are used to focus light, focusing magnets are used in storage rings to focus the electron beam. Using a repeating arrangement of focusing magnets, the beam size can be controlled over the storage ring. So far, the discussion has been limited to electron beams in storage rings, so where does the precious synchrotron light used in experiments come from?

In storage rings, synchrotron light used for experiments is produced in magnetic devices inserted into long empty sections of the ring. These devices are aptly (and again, uncreatively) called insertion devices. Inside insertion devices, there are strong magnetic fields which force beam electrons to wiggle back and forth. High-intensity synchrotron light is produced as a result of electron wiggling, and is then diverted to the experiment. Unfortunately, the magnetic fields inside all real insertion devices come with imperfections. The net result of these imperfections is an undesired change in a number of beam properties. Among them, the beam size. The undesired effects of insertion devices on the beam size can be thought of in analogy to near-sightedness, where rays of light are focused too strongly, and converge at a point in the eye in front of the retina. Analogously, the imperfections in the magnetic fields of insertion devices constitute a focusing error on the electron beam, causing the electron beam to be too strongly focused, reducing the beam size below its intended value.

A common remedy for near-sightedness in humans comes in the form of corrective lenses, either in the form of glasses or contacts. In storage rings, the remedy for focusing errors in insertion devices comes in the shape of focusing magnets. Much like the strengths of corrective lenses need to be determined to remedy each individual case of myopia, the strength of corrective focusing magnets needs to be determined to remedy the focusing error posed by individual insertion devices. Determining the strengths of focusing magnets required to eliminate the focusing error in insertion devices is the main focus of this project.

The required focusing magnet strengths were determined using two different approaches. The first relies on modeling the focusing effect in IDs from theory and solving the problem in simulation. The second approach is different, and was developed as a part of this project. It is an iterative approach, which performs repeated measurements of the beam size, followed by the calculation and application of small adjustments to the focusing magnets. There are two main conclusions in this project: First, the focusing magnet strengths determined by use of the modeling approach are not good enough, and the models used should be investigated. Second: The iterative approach shows promise, and was able to restore beam size in the few tests performed. Though, as this is a freshly-developed technique, further testing is needed.

• author: Schmand, Johann
• supervisor: Francesca Curbis; Magnus Sjöström
• organization: Department of Physics; Synchrotron Radiation Research
• course: FYSM64 20261
• year: 2026
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• language: English
• id: 9245942
• date added to LUP: 2026-07-13 09:42:49
• date last changed: 2026-07-13 09:42:49